I need to alert someone when a new item is created but it wont be the same person each time. I want to pull the name from the current list item and alert them. For example if i had a column in the list called name, and I made a new list item with the name column as "bob". Could i make an alert sent to bob using the alert function? I would like to stay away from SPD.

To be honest even though you said you didn't want to use sharepoint designer, that is really the direction you should go. Having users sign up for their own alerts won't get you the result you are looking for. It will be sending them alerts all the time when new items are created, instead of only when their name is in the 'Name' column.

In sharepoint designer, all you need to do is create a new list workflow. Add the 'Send an Email' action. When you click the 'these users' link in the action name, it will let you set up the email.

Click the little book icon next to the To: box. Select the option "Worklfow Lookup for a User..." and click Add. It will bring up the Lookup for a Person or Group dialog box. Your Data source is the Current List and the Field from Source is the column which stores the person's name (I'm assuming that column is a people picker control). You can 'return field as' Email address and click OK.

Then you just have to write out your email. You can even include information from the list item in the email by using the 'Add or Change Lookup' button at the bottom of the email window.

The workflow only needs one step. You'll just want to set the start options for the workflow to start automatically when an item is created or modified, whichever is appropriate for your needs. Then publish the workflow.

The only other thing to consider is that this solution doesn't give people the choice to 'opt-out' of sending the email. If you wanted people to have that ability, you could just add a checkbox column, then add a condition to the workflow that checks to see if the box was checked or not.

Create a "Person or Group" field in the list (you can't do this with names entered into an ordinary text field).

Create a view on the list called, for example, Assigned to Me, and under the Filter heading of the view's settings, choose "Show items only when the following is true:"Assigned Tois equal to[Me]

Create an alert on the list, but replace your own name in the Send Alerts To field with the names of each individual that should be notified in this manner (of course, if you're one of the people whose name might appear in the field, then leave yourself in the list, too).
Under Change Type, choose "Only send me alerts when:"New items are added
Under Send Alerts for These Changes, choose "Someone changes an item that appears in the following view:"Assigned to Me

Now each person should receive alerts when their own name is entered into the Assigned To field of an item when it is created. The only drawback is that if, for example, a new person joins the team, someone will have to remember that they won't get notified until someone sets up the alert for that person. (Actually, it might be possible to enter a SharePoint group into the Send Alerts To field, which would eliminate this problem, but I haven't tested that.)

Note: I'm pretty sure this alert will not trigger if a user's name is added to the Assigned To field through an edit made to an existing item.